Some sports and games have a notion of a "perfect score."  For example, a perfect score in bowling is 300 (twelve consecutive strikes;) a perfect score in golf would be 18 (18 holes-in-one.)

After watching Watson destroy Ken Jennings and Brad Rutter I began to wonder what a perfect score in Jeopardy! would be.

Assumptions:

  • The player knows (or can guess) all the correct questions for the given answers.
  • The player can consistently beat the other players to the buzzer.
  • The player knows (or can guess) where all three Daily Doubles are.
  • The Daily Double in the Jeopardy! round happens to be on a $200 clue.
  • The two Daily Doubles in the Double Jeopardy! round both happen to be on $400 clues.
  • The player is willing to "bet it all" at all four opportunities (the three Daily Doubles and Final Jeopardy!).

Jeopardy! has three rounds:

  1. The Jeopardy! round
    The player starts this round with $0.
    There are six categories with five clues each: $200, 400, 600, 800, 1000.  That's $3000 for each category for a nominal total of $18,000.
    But wait - one of those clues is a Daily Double!  For maximum value we're assuming it's a $200 clue.
    The player gets all the normal clues correct and amasses $17,800.
    The player then "makes it a true daily double", gets it right, and doubles their total to $35,600.
  2. The Double Jeopardy! round
    The player starts this round with $35,600.  Again, there are six categories with five clues each.  But this time the values are $400, 800, 1200, 1600, and $2000.
    That's $6000 for each category for a nominal total of $36,000.
    But wait - two of those clues are Daily Doubles!  For maximum value we're assuming they're both $400 clues.
    The player gets all the normal clues correct and amasses an additional $35,200.  They now have $70,800.
    The player then selects the first of the two Daily Doubles for this round, "makes it a true daily double", gets it right, and doubles their total to $141,600.  (Jeopardy!, unlike some game shows, does not materialize winnings at the end of a round; there's just a single running total for each player throughout the episode.)
    The player then selects the last Daily Double, "makes it a true daily double", gets it right, and doubles their total to $283,200.
  3. Final Jeopardy!
    The player starts this round with $283,200.
    The player looks at the category, bets everything, looks at the answer, writes down the correct question, and doubles their total to $566,400.

Conclusion: A perfect score for a single episode of Jeopardy! is $566,400.

The actual record appears to be Roger Craig's win of $77,000 on September 14 2010.